(adsbygoogle = window.adsbygoogle || []).push({}); Producing the Ricci tensor

On a pseudo-Riemannian manifold we can contract the Riemann curvature tensor to form the Ricci tensor. In this process of contraction we sum over two indices to make a (3-1)-tensor into a (2-0)-tensor. My question is, why must we contract two indices? Why cant we contract one index to form a (3-0)-tensor or a (2-1)-tensor, etc...

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Producing a Ricci tensor

Loading...

Similar Threads for Producing Ricci tensor | Date |
---|---|

I Basic Q about Vector/tensor definition and velocity | Feb 24, 2018 |

I Covariant derivative of Ricci scalar causing me grief! | Nov 26, 2017 |

A On the dependence of the curvature tensor on the metric | Nov 2, 2017 |

I Ricci curvatures determine Riemann curvatures in 3-dimension | Nov 29, 2016 |

A Notation in Ricci form | Oct 17, 2016 |

**Physics Forums - The Fusion of Science and Community**